Groups with the Minimal Condition on Non-“Nilpotent-by-Finite” Subgroups

We characterize the groups which do not have non-trivial perfect sections and such that any strictly descending chain of non-“nilpotent-by-finite” subgroups is finite

Cofinite derivations in rings

A derivation d : R → R is called cofinite if its image Im d is a subgroup of finite index in the additive group R of an associative ring R. We characterize left Artinian (respectively semiprime) rings with all non-zero inner derivations to be cofinite. Keywords: Derivation, Artinian ring, semiprime ring MSC: 16W25, 16P20, 16N6

Solvable groups with many BFC-subgroups

We characterize the solvable groups without infinite properly ascending chains of non-BFC subgroups and prove that a non-BFC group with a descending chain whose factors are finite or abelian is a Cernikov group or has an infinite properly descending chain of non-BFC subgroups

Differentially trivial left Noetherian rings

summary:We characterize left Noetherian rings which have only trivial derivations

The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of the generalized Riemann type hierarchy are also discussed.Comment: 18 page

Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.Comment: 11 page

Differentially trivial left Noetherian rings

summary:We characterize left Noetherian rings which have only trivial derivations

Rings whose non-zero derivations have finite kernels

We prove that every infinite ring $R$ is either differentially trivial or has a non-zero derivation $d$ with an infinite kernel $Ker\, d$

Left Noetherian rings with differentially trivial proper quotient rings

We characterize left Noetherian rings with differentially trivial proper quotient rings.<br /